First-principles study of oxygen vacancies in LiNbO3-type ferroelectrics

LiNbO3-type ferroelectric oxides, as an important class of non-centrosymmetric compounds, have received great attention due to their important and rich properties. Although oxygen vacancies are widely present, studies of them in LiNbO3-type ferroelectric oxides are rare. In this article, we consider three representative LiNbO3-type ferroelectric oxide materials LiNbO3, ZnTiO3 and ZnSnO3 to study the impact of oxygen vacancy doping using first principles calculations. LiNbO3 and ZnTiO3 have ferroelectrically active cations Nb5+ and Ti4+, while ZnSnO3 does not have ferroelectrically active cations. The distribution of the oxygen vacancy induced electrons are quite different in the three materials even though they have similar structures. In oxygen deficient LiNbO3−δ (δ = 0.083/f.u.), electrons are itinerant, while in ZnTiO3−δ and ZnSnO3−δ (δ = 0.083/f.u.) the electrons are localized. These results provide guidance for the application of oxygen vacancies in LiNbO3-type ferroelectric material devices.


Introduction
2][3][4][5] For example, oxygen vacancies are one of the basic and inherent defects of perovskite oxides and are widely present in perovskite oxides.7][8][9] Experimental and theoretical studies of oxygen vacancies in prototypical perovskite oxides have been reported, such as SrTiO 3 , BaTiO 3 , PbTiO 3 et al. [10][11][12] Usually, it is an effective way to dope electrons in oxides by oxygen vacancies.Oxygen vacancies can be introduced into perovskite oxides through various processes such as growth, annealing, and redox reactions. 13One oxygen vacancy contribute two electrons, which distribute in the materials depend on the properties.For example, oxygen vacancy doping in SrTiO 3 can lead to the transition from insulator to metal. 14However, electrons may be trapped. 15][18] Especially, in polar oxides, the existence of oxygen vacancies has crucial effects on the polarization. 19,20The studies of oxygen vacancies in perovskite ferroelectrics such as BaTiO 3 and PbTiO 3 have been widely reported. 21,22Cheng et al. reported the transformation of oxygen vacancies from an isolated state to a clustered state in LiNbO 3 single crystal, making controlling the oxygen vacancy state a promising option. 23However, apart from LiNbO 3 , there are not many studies on oxygen vacancies in other important polar oxides with LiNbO 3 type (LN type) structure.Recently, more and more LN-type structural materials have been synthesized, such as ZnSnO 3 , 24,25 ZnTiO 3 , 26 ZnPbO 3 , 27 PbNiO 3 . 28Therefore, it is desirable to study the properties of oxygen vacancies and their effects on polar displacements.
For this work, we chose three representative LN-type ABO 3 ferroelectrics LiNbO 3 , ZnTiO 3 and ZnSnO 3 to study the inuence of oxygen vacancy on polarization.ZnSnO 3 does not have ferroelectrically active cations, while ZnTiO 3 has the ferroelectrically active cation Ti 4+ .Compared with ZnTiO 3 and ZnSnO 3 , LiNbO 3 has different chemical valence on both A and B sites.Therefore, the comparison of these three representative LN-type ferroelectrics is helpful to understand the impact of the oxygen vacancy on other LN-type ferroelectrics.Our study shows that, in the three compounds, polar displacements persists at a certain level of oxygen vacancy concentration, but exhibit completely different behaviors.In LiNbO 3 , the electrons induced by oxygen vacancy are itinerant.However, in ZnTiO 3 and ZnSnO 3 they are localized.

Methods and computational details
All rst-principles calculations were performed with the Quantum ESPRESSO code 29 within the local density approximation (LDA).We also used the Perdew-Burke-Ernzerhof functional revised for solids (GGA-PBEsol) 30 to verify our main calculation results.The key results of our calculations did not change qualitatively due to different exchange correlation functions.Detailed results are given in Section IV of the ESI.† 31 The cutoff energy was set to 650 eV.The atomic positions in all structures were relaxed until forces were converged to less than 10 meV Å −1 .The convergence value of the self-consistent calculation was 10 −5 eV.
The LN type structure is closely related to the perovskite oxide type structure and both have three-dimensional cornersharing BO 6 octahedrons.The octahedral rotation of the LNtype ferroelectric with the R3c structure is a − a − a − in Glazer notation.The [111] direction in the pseudo cubic lattice of the Pv-type structure corresponds to the hexagonal c-direction of the LN-type structure.In LN-type compounds, along the c direction of the hexagonal structure, there is a relative displacement of cations relative to the anion layer (oxygen layer), leading to the occurrence of spontaneous polarization, as shown in Fig. 1.We choose the hexagonal structure (30 atoms) of LN-type ferroelectric materials to perform pristine bulk calculations.In Table 1, we list the calculated and experimental lattice parameters of the hexagonal unit cells of these three materials.We can see that our calculated results are consistent with the experimental results.
We use supercell calculations to simulate charge neutral oxygen vacancies.To simulate oxygen-decient LiNbO 3−d , ZnTiO 3−d , and ZnSnO 3−d , we start from the R3c structure of pristine LN-type ferroelectric and remove one charge-neutral oxygen atom.In the R3c LN-type ferroelectric structure, all oxygen atoms positions are equivalent and there is only one Wyckoff position.To study the distribution of electrons induced by the oxygen vacancy, we perform calculations on a supercell of 59-atom, which corresponds to an oxygen vacancy concentration of 0.083/f.u. and electron doping concentration of 0.17 e/ f.u. 4 × 2 × 2 and 12 × 6 × 6 Monkhorst-Pack k-point grids are used for the calculation of structural relaxation and density of states (DOS), respectively.We perform spin polarization calculations in pristine LiNbO 3 , ZnTiO 3 and ZnSnO 3 , as well as oxygen-decient LiNbO 3−d , ZnTiO 3−d and ZnSnO 3−d .As shown in Fig. S1 in the ESI, † 31 DOS did not show any magnetization in our calculations.Therefore, we sum the two spins when calculating DOS.We fully relax the structure including lattice constants and internal coordinates to obtain the ground state structure.Using the VESTA soware package, 32 we visualize the crystal structure and iso-surfaces of the charge distribution.
With oxygen vacancy, the polarization cannot be calculated using the Berry phase method due to the existence of free charge.Therefore, we focus on analyzing the polar displacement of cations and anions.For the polarized R3c structure, taking LiNbO 3 as an example as shown by Fig. 1

Results and discussion
First, we analyze the electronic structures of the three materials without oxygen vacancies.Fig. 2 shows the total density of states   Compared with ZnTiO 3 , the contribution of Sn atoms to VB in ZnSnO 3 is smaller, as shown by the blue curves in Fig. 2(c) and (e).The BEC can reect the covalency of each atom's bonding environment relative to its nominal ionic value. 36As shown in Table 2, the BEC of Nb in LiNbO 3 deviates most from the nominal charge (+5).The BEC of Ti in ZnTiO 3 deviates less from the nominal charge (+4).The BEC of Sn in ZnSnO 3 is almost consistent with the nominal charge (+4), and the deviation is very small.Furthermore, it is also evident from Table 2 that cations with d 0 (Nb 5+ and Ti 4+ ) electron conguration have larger BEC values than the corresponding nominal charges than cations with d 10 (Zn 2+ and Sn 4+ ) electron conguration.
We next compare the electronic structures of oxygen-decient LiNbO   are consistent with previous studies. 39The reduction of the polar displacement is because of the electrons induced by the oxygen vacancies.The uniformly distributed free electrons in the whole system on the Nb-d orbitals has screening effects on the long-range Coulomb interaction which is responsible to the polarization.
For oxygen-decient ZnTiO where E defect (V O ) and E ideal are the total energies of the supercell with one oxygen vacancy and the pristine supercell without oxygen vacancy respectively.m O is the chemical potential of oxygen, which depends on the thermodynamic conditions of the system which is half the total energy of the oxygen molecule. 41e use different supercells to calculate the oxygen vacancy formation energy at different concentrations.We consider 30 atoms, 60 atoms, and 120 atoms hexagonal supercells, as well as 80 atoms rhombohedral supercell, and schematics of these structures are in Fig. S4 in ESI.† 31 We remove one charge-neutral oxygen atom in these structures and the oxygen vacancy concentrations are d = 0.167/f.u., 0.083/f.u., 0.042/f.u. and 0.063/f.u., respectively.Fig. 5 shows the oxygen vacancy formation energy as a function of oxygen vacancy concentration.
We see that the change of oxygen vacancy concentration has no signicant impact on the formation energy of oxygen vacancies.The formation energy of LiNbO 3 is relatively close to the neutral oxygen vacancy formation energy of tetragonal BaTiO 3 of 6.35 eV. 42The formation energy of LiNbO 3 and ZnTiO 3 are much higher than that of ZnSnO 3 .Probably it is due to the covalent bonding between Nb-O and Ti-O are stronger than Sn-O as shown in Fig. 2.Even though the formation energy of oxygen vacancies in LiNbO 3−d is higher, oxygen vacancies were observed in the experiments. 43,44There have been experimental reports on the study of oxygen vacancies in ZnSnO 3 . 45It is reported that the oxygen vacancies in ferroelectric ZnSnO 3 nanowires can serve as exciton capture centers, and the deep energy levels serve as donor bands, enhancing electron lifetime and effectively promoting electrons to reach CB under light irradiation.We can expect that similar studies in LN-type ferroelectric oxides can expand our understanding of the behavior of oxygen vacancies and provide guidance for the application of specic oxygen vacancy properties in new devices.

Conclusion
In conclusion, we use rst-principles calculations to study the effect of oxygen vacancy doping on three representative LN-type ferroelectric oxide materials.LiNbO 3 and ZnTiO 3 have ferroelectrically active cations Nb 5+ and Ti 4+ , while ZnSnO 3 does not have ferroelectrically active cations.With comparison, we study the distribution of the oxygen vacancy induced electrons.Our results show that in oxygen-decient LiNbO 3−d , electrons are itinerant.Although the polar displacement is reduced by oxygen vacancy doping, polar displacements and conductivity can coexist in LiNbO 3−d .However, in oxygen-decient ZnTiO 3−d and ZnSnO 3−d electrons are localized around the oxygen vacancy.To realize conducting ferroelectric in ZnTiO 3 and ZnSnO 3 , doping oxygen vacancy probably is not an effective way.
, the Li atom at A site is surrounded by three O atoms in the same plane.The relative displacement between the Li atom and the center of the three oxygen atoms in the c-axis direction is recorded as d Li−O .While the relative displacement between the Nb atom and the center of the surrounding six O atoms along the c-axis direction is recorded as d Nb−O .When an oxygen atom is removed, there is one Li atom with only two nearest O atoms, and two Nb atoms surrounded by the ve nearest O atoms.
3−d , ZnTiO 3−d and ZnSnO 3−d (d = 0.083/f.u.), as shown in Fig. 2(b), (d) and (f).In Fig. S5 in the ESI, † 31 we provide a detailed comparison of the band gaps calculated by LDA, HSE06, and PBEsol for bulk LiNbO 3 , ZnTiO 3 , and ZnSnO 3 .In Fig. 2(a), the band gap of LiNbO 3 we calculated is 3.3 eV, which is close to the experimental value of 3.78 eV of LiNbO 3 . 37This is consistent with previous calculations and the gap results are reliable. 38However, we nd that for oxygen-decient LiNbO 3−d (d = 0.083/f.u.), the Fermi level moves into the CB, and no additional localized states appear in the band gap, as shown in Fig. 2(b).The oxygen-decient LiNbO 3−d is a conductor with electrons distribute overall the system.While ZnTiO 3−d and ZnSnO 3−d are insulators with electrons localized around the oxygen vacancy.For oxygen-decient ZnTiO 3−d and ZnSnO 3−d (d = 0.083/f.u.), we can see localized states in the band gap at 0.50 and 0.75 eV below the conduction band minimum (CBM), as shown by Fig. 2(b) and (f).The distribution of defect states can be clearly seen in Fig. S3 in the ESI.† 31 Each oxygen vacancy contributes two electrons to the system, and then we study the distribution of the electrons.In Fig. 2(b), our integrated value for the total DOS of oxygen-decient LiNbO 3−d (d = 0.083/f.u.) from the band gap to the Fermi level is 2, and the two electrons provided by the oxygen vacancy occupy the conduction band.In Fig. 2(d) and (f), for oxygen-decient ZnTiO 3−d and ZnSnO 3−d (d = 0.083/f.u.), we integrate the total DOS of the localized states in the band gap to get a value of 2, which means that two electrons occupy the defect state.The spatial distribution of oxygen vacancy doping electrons in these three materials can be seen more clearly from Fig. 3.For oxygen-decient LiNbO 3−d (d = 0.083/f.u.), since the conduction band is contributed by the Nb-d orbital, electrons are mainly distributed uniformly on Nb sites, which is clearly
3−d and ZnSnO 3−d (d = 0.083/f.u.), due to the localization of the oxygen vacancy induced electrons, we cannot see overall reduction of the polar displacement as that in LiNbO 3−d (d = 0.083/f.u.).There is only obvious changing of the polar displacements on atoms that are close to the oxygen vacancy.For oxygen-decient ZnTiO 3−d (d = 0.083/f.u.) as shown in Fig. 4(b), the nearest neighbor Zn atom of the oxygen vacancy is labeled 8, and the second nearest neighbor Zn atom is labeled 5.The nearest neighbor Ti atom of the oxygen vacancy is labeled 6, and the second nearest neighbor Ti atom is labeled 7.As shown in Fig. 4(c), for oxygen-decient ZnSnO 3−d (d = 0.083/ f.u.), the nearest neighbor Zn atom is labeled 8, and the second nearest neighbor Zn atom is labeled 5.The nearest neighbor Sn atom is labeled 8, and the second nearest neighbor Sn atom is labeled 9. Except for the large changes in the nearest neighbor and second nearest neighbor atomic displacements of the oxygen vacancy, the atomic displacements at other positions are close to the displacements of the pristine ZnTiO 3 and ZnSnO 3 .This is because the localization of the electrons does not have screening effect in the whole structure.Finally, we calculate the formation energies of charge neutral oxygen vacancy of LiNbO 3−d , ZnTiO 3−d and ZnSnO 3−d .We remove a single oxygen atom in the supercell.The oxygen vacancy formation energy is dened as,40

Fig. 4
Fig. 4 Polar displacements of each Li atom, Nb atom, Zn atom, Ti atom and Sn atom in oxygen-deficient (a) LiNbO 3−d , (b) ZnTiO 3−d and (c) ZnSnO 3−d (d = 0.083/f.u.), respectively.Solid circles and squares are for the oxygen-deficient structures while the open circles and squares are for the pristine structures.